/*
 * Copying and distribution of this file, with or without modification,
 * are permitted in any medium without royalty provided the copyright
 * notice and this notice are preserved.  This file is offered as-is,
 * without any warranty.
 *
 * author: Francois-Michel De Rainville
 * version: 0.2.0
 * date: 23/03/2011
 */

#define HALTON_MAX_DIMENSION 1229

static const unsigned int PRIMES[HALTON_MAX_DIMENSION] = {
2, 3, 5, 7, 11, 13, 17, 19, 23, 29,
31, 37, 41, 43, 47, 53, 59, 61, 67, 71,
73, 79, 83, 89, 97, 101, 103, 107, 109, 113,
127, 131, 137, 139, 149, 151, 157, 163, 167, 173,
179, 181, 191, 193, 197, 199, 211, 223, 227, 229,
233, 239, 241, 251, 257, 263, 269, 271, 277, 281,
283, 293, 307, 311, 313, 317, 331, 337, 347, 349,
353, 359, 367, 373, 379, 383, 389, 397, 401, 409,
419, 421, 431, 433, 439, 443, 449, 457, 461, 463,
467, 479, 487, 491, 499, 503, 509, 521, 523, 541,
547, 557, 563, 569, 571, 577, 587, 593, 599, 601,
607, 613, 617, 619, 631, 641, 643, 647, 653, 659,
661, 673, 677, 683, 691, 701, 709, 719, 727, 733,
739, 743, 751, 757, 761, 769, 773, 787, 797, 809,
811, 821, 823, 827, 829, 839, 853, 857, 859, 863,
877, 881, 883, 887, 907, 911, 919, 929, 937, 941,
947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013,
1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069,
1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151,
1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223,
1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291,
1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373,
1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451,
1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511,
1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583,
1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657,
1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733,
1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811,
1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889,
1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987,
1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053,
2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129,
2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213,
2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287,
2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357,
2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423,
2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531,
2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617,
2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687,
2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741,
2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819,
2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903,
2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999,
3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079,
3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181,
3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257,
3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331,
3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413,
3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511,
3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571,
3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643,
3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727,
3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821,
3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907,
3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989,
4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057,
4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139,
4153, 4157, 4159, 4177, 4201, 4211, 4217, 4219, 4229, 4231,
4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297,
4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409,
4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493,
4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583,
4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657,
4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751,
4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831,
4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937,
4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003,
5009, 5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087,
5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179,
5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279,
5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387,
5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443,
5449, 5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521,
5527, 5531, 5557, 5563, 5569, 5573, 5581, 5591, 5623, 5639,
5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693,
5701, 5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791,
5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857,
5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939,
5953, 5981, 5987, 6007, 6011, 6029, 6037, 6043, 6047, 6053,
6067, 6073, 6079, 6089, 6091, 6101, 6113, 6121, 6131, 6133,
6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221,
6229, 6247, 6257, 6263, 6269, 6271, 6277, 6287, 6299, 6301,
6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367,
6373, 6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473,
6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571,
6577, 6581, 6599, 6607, 6619, 6637, 6653, 6659, 6661, 6673,
6679, 6689, 6691, 6701, 6703, 6709, 6719, 6733, 6737, 6761,
6763, 6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833,
6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917,
6947, 6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997,
7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103,
7109, 7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207,
7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283, 7297,
7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411,
7417, 7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 7499,
7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561,
7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 7643,
7649, 7669, 7673, 7681, 7687, 7691, 7699, 7703, 7717, 7723,
7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829,
7841, 7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919,
7927, 7933, 7937, 7949, 7951, 7963, 7993, 8009, 8011, 8017,
8039, 8053, 8059, 8069, 8081, 8087, 8089, 8093, 8101, 8111,
8117, 8123, 8147, 8161, 8167, 8171, 8179, 8191, 8209, 8219,
8221, 8231, 8233, 8237, 8243, 8263, 8269, 8273, 8287, 8291,
8293, 8297, 8311, 8317, 8329, 8353, 8363, 8369, 8377, 8387,
8389, 8419, 8423, 8429, 8431, 8443, 8447, 8461, 8467, 8501,
8513, 8521, 8527, 8537, 8539, 8543, 8563, 8573, 8581, 8597,
8599, 8609, 8623, 8627, 8629, 8641, 8647, 8663, 8669, 8677,
8681, 8689, 8693, 8699, 8707, 8713, 8719, 8731, 8737, 8741,
8747, 8753, 8761, 8779, 8783, 8803, 8807, 8819, 8821, 8831,
8837, 8839, 8849, 8861, 8863, 8867, 8887, 8893, 8923, 8929,
8933, 8941, 8951, 8963, 8969, 8971, 8999, 9001, 9007, 9011,
9013, 9029, 9041, 9043, 9049, 9059, 9067, 9091, 9103, 9109,
9127, 9133, 9137, 9151, 9157, 9161, 9173, 9181, 9187, 9199,
9203, 9209, 9221, 9227, 9239, 9241, 9257, 9277, 9281, 9283,
9293, 9311, 9319, 9323, 9337, 9341, 9343, 9349, 9371, 9377,
9391, 9397, 9403, 9413, 9419, 9421, 9431, 9433, 9437, 9439,
9461, 9463, 9467, 9473, 9479, 9491, 9497, 9511, 9521, 9533,
9539, 9547, 9551, 9587, 9601, 9613, 9619, 9623, 9629, 9631,
9643, 9649, 9661, 9677, 9679, 9689, 9697, 9719, 9721, 9733,
9739, 9743, 9749, 9767, 9769, 9781, 9787, 9791, 9803, 9811,
9817, 9829, 9833, 9839, 9851, 9857, 9859, 9871, 9883, 9887,
9901, 9907, 9923, 9929, 9931, 9941, 9949, 9967, 9973
};

static const unsigned int EA_PERMS[24133] = {
0, 1,
0, 2, 1,
0, 4, 2, 3, 1,
0, 6, 5, 4, 3, 2, 1,
0, 8, 2, 10, 4, 9, 5, 6, 1, 7, 3,
0, 10, 9, 5, 12, 3, 8, 4, 11, 7, 6, 2, 1,
0, 16, 11, 2, 12, 8, 7, 5, 15, 6, 3, 13, 9, 1, 10, 14, 4,
0, 8, 6, 1, 15, 7, 3, 16, 17, 11, 14, 18, 5, 9, 13, 4, 2, 10, 12,
0, 8, 1, 17, 13, 5, 16, 9, 6, 22, 18, 10, 21, 3, 12, 20, 4, 11, 19, 2, 14, 7, 15,
0, 21, 14, 8, 28, 2, 24, 10, 5, 27, 9, 26, 4, 25, 17, 1, 18, 7, 11, 19, 23, 15, 3, 20, 12, 22, 13, 6, 16,
0, 22, 15, 24, 7, 28, 5, 18, 20, 14, 16, 10, 25, 2, 11, 9, 19, 17, 29, 26, 4, 12, 23, 8, 1, 21, 30, 6, 13, 3, 27,
0, 23, 32, 3, 18, 22, 25, 15, 12, 8, 20, 34, 27, 19, 30, 6, 4, 33, 28, 36, 1, 10, 13, 9, 5, 35, 26, 29, 31, 21, 17, 16, 24, 7, 11, 14, 2,
0, 15, 39, 24, 11, 38, 1, 16, 32, 10, 20, 26, 12, 28, 27, 14, 5, 29, 6, 30, 21, 13, 19, 23, 18, 8, 25, 3, 36, 34, 31, 33, 22, 4, 35, 17, 2, 37, 9, 7, 40,
0, 34, 7, 17, 10, 25, 39, 40, 42, 16, 38, 18, 36, 27, 37, 15, 32, 11, 2, 24, 35, 41, 33, 3, 6, 23, 22, 28, 29, 30, 20, 8, 4, 19, 21, 31, 9, 1, 5, 12, 13, 14, 26,
0, 14, 9, 36, 38, 20, 41, 8, 25, 19, 28, 33, 46, 22, 30, 12, 37, 5, 35, 32, 44, 16, 10, 11, 3, 6, 23, 42, 17, 39, 18, 26, 4, 34, 43, 31, 21, 45, 27, 2, 7, 13, 1, 24, 15, 40, 29,
0, 7, 33, 48, 18, 1, 13, 47, 29, 9, 5, 14, 51, 3, 49, 32, 4, 16, 39, 12, 31, 28, 11, 17, 23, 40, 37, 30, 15, 21, 36, 52, 45, 35, 20, 41, 38, 43, 26, 24, 27, 10, 42, 50, 25, 19, 34, 2, 46, 22, 44, 8, 6,
0, 20, 44, 56, 17, 53, 12, 24, 13, 33, 19, 51, 40, 45, 1, 9, 36, 23, 18, 27, 41, 31, 47, 43, 57, 10, 38, 14, 2, 30, 46, 54, 6, 49, 34, 16, 11, 15, 29, 52, 25, 58, 8, 42, 50, 3, 35, 26, 39, 22, 48, 4, 55, 7, 37, 5, 28, 21, 32,
0, 22, 26, 5, 36, 60, 57, 59, 30, 12, 11, 13, 19, 29, 56, 58, 4, 35, 3, 25, 32, 43, 48, 16, 45, 33, 10, 23, 15, 50, 7, 14, 52, 8, 9, 6, 42, 46, 40, 47, 27, 34, 39, 2, 20, 41, 21, 54, 28, 44, 38, 49, 55, 53, 51, 18, 31, 37, 17, 24, 1,
0, 46, 63, 18, 59, 48, 58, 61, 50, 24, 3, 12, 15, 11, 14, 10, 32, 54, 7, 56, 49, 44, 6, 38, 53, 30, 37, 39, 36, 34, 5, 21, 52, 41, 66, 26, 64, 29, 9, 57, 60, 16, 17, 23, 55, 62, 19, 2, 43, 33, 8, 42, 47, 31, 65, 51, 40, 1, 20, 13, 28, 22, 4, 25, 45, 27, 35,
0, 63, 32, 27, 31, 67, 49, 43, 51, 56, 22, 55, 66, 29, 11, 65, 60, 8, 39, 37, 40, 18, 2, 30, 24, 36, 35, 48, 17, 16, 58, 62, 12, 26, 47, 3, 54, 33, 68, 34, 28, 1, 46, 69, 53, 61, 42, 59, 13, 25, 14, 5, 64, 4, 23, 15, 45, 20, 10, 9, 44, 41, 21, 38, 57, 52, 7, 19, 70, 6, 50,
0, 31, 36, 17, 29, 12, 69, 52, 2, 20, 57, 45, 48, 39, 59, 13, 63, 8, 15, 64, 65, 43, 54, 38, 6, 11, 41, 51, 37, 61, 33, 35, 23, 62, 9, 1, 22, 55, 5, 58, 47, 7, 71, 60, 46, 3, 21, 16, 56, 66, 14, 24, 53, 44, 40, 4, 50, 49, 28, 34, 10, 26, 18, 25, 72, 67, 70, 30, 27, 42, 32, 68, 19,
0, 28, 59, 6, 76, 72, 11, 31, 50, 12, 62, 35, 14, 57, 77, 22, 44, 78, 67, 38, 23, 43, 13, 21, 41, 32, 45, 29, 61, 48, 74, 69, 16, 27, 51, 60, 37, 56, 5, 10, 8, 18, 49, 4, 58, 54, 15, 2, 55, 17, 68, 40, 3, 53, 36, 65, 39, 7, 66, 24, 19, 64, 73, 46, 9, 33, 20, 63, 47, 1, 71, 52, 25, 70, 34, 26, 42, 30, 75,
0, 71, 4, 58, 46, 36, 29, 31, 74, 79, 81, 41, 50, 63, 48, 33, 38, 80, 21, 20, 2, 55, 54, 73, 64, 75, 52, 19, 32, 12, 53, 59, 57, 45, 67, 47, 26, 6, 78, 49, 61, 34, 7, 24, 76, 62, 69, 18, 5, 22, 9, 8, 35, 56, 68, 70, 3, 10, 11, 15, 27, 1, 82, 72, 65, 66, 23, 39, 40, 77, 14, 25, 28, 60, 44, 43, 42, 51, 13, 16, 17, 30, 37,
0, 41, 82, 65, 1, 68, 33, 10, 46, 8, 58, 87, 32, 78, 13, 28, 2, 76, 20, 66, 38, 83, 56, 80, 84, 52, 25, 49, 34, 75, 51, 21, 67, 48, 71, 81, 23, 31, 36, 74, 88, 54, 59, 72, 3, 43, 6, 63, 4, 53, 16, 15, 64, 73, 42, 57, 30, 27, 86, 29, 14, 47, 70, 17, 35, 61, 39, 69, 55, 79, 11, 45, 44, 7, 40, 5, 18, 12, 62, 77, 85, 22, 37, 26, 60, 24, 50, 19, 9,
0, 68, 37, 71, 2, 88, 55, 64, 42, 40, 20, 95, 12, 69, 83, 51, 52, 33, 47, 45, 48, 16, 4, 63, 62, 59, 89, 30, 93, 26, 31, 58, 7, 9, 79, 23, 34, 82, 49, 43, 76, 75, 36, 10, 94, 65, 28, 3, 84, 27, 57, 1, 8, 38, 53, 44, 15, 18, 14, 24, 80, 29, 32, 74, 92, 54, 5, 86, 81, 19, 61, 96, 25, 11, 77, 66, 60, 90, 72, 13, 17, 50, 56, 91, 46, 78, 87, 73, 67, 35, 41, 21, 85, 39, 70, 22, 6,
0, 39, 91, 88, 22, 32, 75, 58, 7, 13, 49, 37, 36, 42, 55, 53, 71, 77, 5, 6, 15, 62, 85, 83, 94, 73, 57, 86, 25, 28, 17, 8, 4, 20, 29, 54, 52, 99, 26, 72, 64, 96, 14, 66, 78, 63, 60, 90, 2, 89, 41, 9, 68, 70, 76, 11, 40, 50, 47, 24, 1, 97, 100, 48, 23, 30, 61, 69, 74, 81, 80, 95, 84, 10, 3, 18, 19, 43, 59, 16, 65, 46, 98, 93, 12, 67, 27, 44, 21, 34, 35, 38, 56, 51, 82, 87, 92, 33, 31, 79, 45,
0, 16, 31, 100, 46, 57, 48, 63, 98, 52, 35, 51, 28, 26, 72, 17, 37, 38, 89, 59, 5, 2, 23, 13, 32, 22, 54, 101, 92, 85, 68, 70, 21, 91, 25, 24, 86, 94, 33, 20, 60, 62, 88, 78, 29, 39, 83, 49, 61, 4, 11, 7, 84, 1, 65, 41, 53, 99, 82, 15, 18, 30, 3, 58, 67, 76, 79, 77, 81, 9, 19, 47, 8, 56, 87, 55, 102, 93, 73, 10, 50, 45, 36, 43, 96, 34, 95, 90, 44, 14, 42, 80, 27, 69, 40, 12, 97, 66, 6, 64, 71, 75, 74,
0, 2, 19, 63, 106, 30, 75, 53, 3, 102, 14, 77, 37, 23, 51, 92, 91, 81, 49, 17, 56, 60, 99, 84, 5, 7, 48, 29, 57, 65, 88, 101, 12, 4, 45, 47, 26, 80, 90, 70, 1, 61, 15, 100, 94, 46, 79, 55, 33, 97, 8, 39, 27, 64, 104, 25, 28, 42, 98, 9, 74, 76, 83, 93, 69, 31, 24, 71, 103, 95, 41, 16, 35, 54, 22, 43, 40, 34, 78, 62, 6, 72, 66, 44, 59, 68, 13, 21, 86, 105, 36, 89, 18, 11, 38, 85, 87, 50, 96, 73, 52, 20, 67, 58, 10, 82, 32,
0, 85, 75, 90, 22, 6, 44, 105, 65, 45, 57, 20, 84, 77, 51, 40, 4, 95, 14, 16, 70, 41, 76, 89, 98, 68, 73, 88, 38, 46, 15, 30, 28, 11, 107, 3, 25, 50, 96, 66, 62, 104, 67, 21, 39, 102, 64, 27, 93, 43, 42, 103, 26, 7, 47, 33, 80, 18, 108, 59, 61, 63, 53, 19, 1, 87, 56, 82, 12, 52, 2, 71, 9, 92, 34, 69, 91, 74, 58, 78, 8, 101, 60, 94, 13, 54, 55, 29, 83, 10, 49, 5, 72, 48, 99, 106, 17, 23, 86, 24, 81, 100, 37, 35, 79, 97, 32, 36, 31,
0, 11, 94, 95, 81, 53, 109, 56, 111, 43, 74, 101, 30, 65, 103, 29, 50, 15, 83, 67, 105, 51, 64, 14, 100, 47, 39, 21, 97, 96, 16, 46, 69, 24, 59, 58, 62, 98, 22, 26, 86, 54, 12, 48, 49, 73, 104, 112, 44, 91, 77, 99, 3, 78, 45, 102, 63, 40, 38, 68, 37, 25, 6, 20, 93, 23, 33, 72, 17, 87, 28, 42, 66, 106, 85, 18, 5, 10, 110, 32, 89, 19, 92, 84, 27, 52, 75, 13, 7, 35, 57, 31, 71, 4, 61, 60, 70, 34, 41, 2, 108, 36, 55, 8, 9, 90, 82, 88, 107, 80, 1, 79, 76,
0, 74, 93, 75, 105, 112, 92, 41, 13, 99, 59, 6, 17, 34, 85, 25, 53, 60, 18, 26, 115, 58, 51, 72, 44, 116, 121, 23, 3, 12, 1, 40, 39, 65, 55, 46, 73, 33, 101, 122, 109, 118, 87, 117, 24, 56, 113, 16, 8, 19, 7, 45, 14, 10, 102, 36, 80, 42, 37, 69, 11, 67, 29, 5, 54, 38, 100, 30, 71, 126, 43, 68, 70, 78, 48, 106, 62, 32, 104, 119, 21, 83, 123, 31, 94, 103, 111, 15, 50, 120, 110, 86, 124, 89, 35, 49, 20, 82, 114, 4, 52, 125, 79, 88, 90, 84, 57, 64, 28, 108, 27, 22, 47, 76, 97, 95, 61, 96, 9, 63, 81, 2, 66, 77, 107, 91, 98,
0, 36, 109, 121, 95, 84, 70, 54, 21, 38, 119, 57, 74, 73, 123, 69, 114, 59, 65, 58, 96, 9, 52, 116, 17, 61, 31, 49, 35, 44, 97, 91, 39, 92, 30, 37, 64, 40, 76, 34, 18, 19, 5, 63, 55, 107, 24, 129, 23, 10, 110, 42, 111, 8, 130, 120, 22, 115, 1, 87, 103, 88, 41, 60, 80, 102, 79, 71, 56, 53, 100, 118, 67, 50, 6, 62, 117, 128, 51, 32, 16, 28, 86, 45, 81, 66, 82, 27, 105, 43, 47, 89, 20, 99, 94, 4, 85, 2, 126, 25, 104, 72, 3, 108, 26, 112, 83, 101, 75, 98, 7, 106, 90, 15, 127, 125, 14, 33, 122, 77, 68, 48, 11, 29, 93, 78, 46, 113, 13, 12, 124,
0, 34, 67, 60, 81, 132, 122, 18, 124, 89, 123, 6, 13, 126, 75, 29, 77, 8, 55, 15, 99, 78, 105, 5, 35, 22, 21, 51, 7, 96, 4, 118, 95, 52, 37, 41, 120, 82, 117, 97, 94, 115, 61, 74, 101, 30, 2, 127, 135, 102, 62, 136, 73, 98, 66, 106, 76, 85, 36, 33, 68, 128, 26, 47, 48, 72, 91, 19, 130, 40, 57, 134, 16, 103, 23, 84, 12, 108, 131, 80, 25, 113, 88, 39, 38, 114, 64, 46, 129, 133, 111, 112, 83, 110, 27, 43, 59, 50, 107, 58, 20, 70, 100, 56, 28, 93, 63, 49, 121, 53, 44, 17, 1, 42, 79, 109, 31, 54, 9, 45, 104, 125, 11, 24, 116, 119, 92, 69, 71, 86, 14, 10, 65, 3, 90, 87, 32,
0, 104, 95, 19, 46, 41, 84, 136, 78, 131, 70, 85, 42, 21, 45, 118, 34, 105, 133, 94, 129, 130, 124, 39, 82, 89, 113, 18, 37, 83, 4, 100, 74, 117, 24, 52, 30, 29, 112, 51, 92, 134, 2, 88, 91, 61, 128, 103, 5, 87, 57, 15, 123, 67, 48, 119, 73, 97, 108, 27, 77, 79, 76, 8, 90, 26, 16, 116, 12, 54, 81, 80, 7, 11, 31, 9, 110, 60, 63, 72, 137, 114, 135, 122, 40, 49, 101, 98, 44, 47, 6, 125, 120, 43, 35, 38, 59, 23, 64, 106, 102, 22, 13, 126, 99, 25, 86, 68, 71, 66, 32, 14, 3, 109, 132, 50, 28, 53, 107, 115, 138, 17, 20, 56, 75, 36, 111, 55, 65, 121, 93, 127, 69, 58, 62, 1, 33, 96, 10,
0, 2, 12, 114, 75, 108, 118, 13, 25, 3, 109, 63, 7, 117, 102, 82, 65, 32, 96, 116, 34, 27, 99, 147, 124, 125, 140, 145, 68, 138, 33, 105, 67, 48, 80, 121, 61, 91, 115, 22, 97, 23, 71, 10, 41, 86, 92, 111, 93, 127, 52, 135, 88, 144, 6, 123, 46, 132, 146, 119, 136, 47, 77, 112, 9, 54, 106, 129, 28, 55, 76, 126, 113, 56, 73, 89, 51, 44, 59, 90, 95, 110, 30, 137, 42, 139, 85, 101, 128, 74, 58, 98, 29, 79, 143, 64, 87, 131, 14, 122, 57, 130, 70, 45, 94, 83, 35, 4, 142, 49, 36, 104, 31, 24, 17, 38, 26, 72, 66, 19, 148, 53, 16, 120, 39, 141, 62, 37, 78, 40, 84, 1, 11, 107, 50, 134, 133, 5, 103, 69, 15, 100, 43, 60, 20, 81, 8, 18, 21,
0, 55, 16, 64, 56, 98, 76, 1, 87, 41, 129, 142, 30, 99, 106, 80, 18, 103, 109, 67, 88, 37, 105, 31, 101, 111, 13, 54, 23, 3, 27, 52, 43, 19, 73, 123, 53, 120, 77, 72, 65, 35, 32, 81, 113, 22, 116, 119, 83, 17, 147, 33, 86, 91, 94, 133, 128, 92, 5, 10, 58, 143, 49, 71, 20, 8, 115, 127, 11, 144, 45, 139, 90, 44, 61, 74, 69, 118, 28, 148, 84, 6, 141, 135, 131, 146, 130, 47, 42, 60, 48, 66, 89, 75, 38, 26, 102, 14, 9, 36, 132, 12, 34, 149, 100, 108, 126, 70, 145, 51, 136, 62, 140, 150, 124, 95, 4, 39, 137, 57, 29, 2, 63, 59, 24, 50, 46, 79, 122, 138, 21, 107, 125, 96, 7, 114, 25, 78, 97, 134, 85, 121, 93, 15, 112, 40, 104, 117, 82, 68, 110,
0, 76, 17, 4, 143, 101, 73, 77, 16, 27, 108, 129, 55, 37, 125, 95, 63, 2, 87, 14, 41, 11, 20, 80, 32, 54, 147, 44, 33, 62, 106, 1, 84, 85, 31, 24, 94, 149, 47, 133, 18, 12, 142, 107, 15, 42, 51, 75, 123, 98, 13, 156, 120, 3, 114, 57, 150, 50, 67, 128, 135, 145, 110, 141, 99, 91, 9, 28, 61, 105, 21, 56, 112, 66, 64, 88, 104, 68, 148, 136, 97, 118, 113, 78, 96, 140, 70, 154, 111, 60, 122, 89, 153, 25, 43, 121, 132, 29, 38, 46, 90, 82, 72, 93, 79, 7, 10, 131, 115, 74, 146, 117, 19, 81, 45, 127, 65, 34, 126, 58, 39, 124, 155, 119, 116, 52, 134, 36, 86, 92, 103, 26, 152, 138, 40, 109, 139, 48, 5, 83, 35, 100, 151, 8, 22, 30, 6, 144, 53, 102, 49, 59, 71, 137, 130, 69, 23,
0, 81, 105, 14, 146, 18, 86, 46, 67, 135, 74, 114, 126, 143, 70, 100, 29, 17, 107, 156, 96, 83, 141, 69, 154, 3, 56, 65, 34, 21, 138, 9, 57, 123, 120, 131, 16, 49, 93, 42, 63, 76, 8, 145, 6, 161, 37, 68, 132, 47, 55, 43, 1, 41, 157, 99, 75, 24, 78, 121, 158, 84, 12, 97, 103, 118, 104, 72, 5, 11, 106, 152, 13, 137, 94, 59, 44, 98, 127, 35, 160, 50, 61, 119, 88, 15, 139, 144, 111, 77, 51, 31, 134, 151, 10, 60, 115, 33, 7, 23, 38, 48, 122, 58, 149, 129, 110, 53, 36, 26, 28, 20, 82, 39, 155, 148, 153, 19, 130, 140, 142, 150, 4, 27, 40, 2, 66, 117, 52, 124, 112, 91, 108, 73, 95, 22, 128, 79, 87, 109, 125, 133, 159, 90, 45, 25, 89, 64, 101, 54, 62, 116, 80, 32, 162, 92, 85, 113, 71, 30, 136, 102, 147,
0, 99, 153, 86, 5, 76, 120, 67, 57, 142, 123, 6, 119, 104, 72, 129, 109, 125, 70, 16, 124, 34, 126, 53, 73, 63, 14, 8, 29, 39, 128, 65, 56, 111, 88, 32, 49, 90, 163, 62, 27, 159, 133, 83, 64, 2, 102, 112, 107, 33, 61, 94, 131, 98, 55, 154, 149, 50, 130, 28, 121, 21, 155, 44, 89, 137, 117, 93, 122, 38, 59, 116, 156, 43, 105, 148, 101, 150, 1, 22, 138, 81, 3, 136, 24, 166, 87, 54, 15, 60, 66, 118, 151, 132, 37, 145, 48, 103, 91, 11, 78, 134, 12, 108, 146, 4, 158, 75, 82, 143, 51, 20, 46, 160, 52, 115, 35, 58, 74, 141, 152, 69, 30, 92, 140, 80, 71, 157, 135, 147, 100, 10, 19, 23, 127, 161, 95, 31, 96, 36, 139, 165, 110, 26, 84, 13, 106, 85, 162, 42, 25, 41, 144, 114, 164, 68, 45, 77, 40, 9, 18, 79, 47, 7, 97, 113, 17,
0, 18, 157, 167, 10, 56, 112, 41, 87, 169, 2, 7, 80, 11, 61, 47, 90, 76, 155, 115, 101, 49, 26, 3, 164, 113, 172, 32, 59, 114, 123, 74, 36, 89, 70, 97, 150, 135, 103, 144, 146, 34, 118, 13, 151, 158, 31, 40, 30, 121, 43, 84, 72, 126, 141, 69, 25, 33, 63, 71, 65, 107, 48, 159, 22, 154, 110, 139, 102, 15, 60, 83, 64, 105, 168, 117, 9, 54, 100, 45, 42, 130, 75, 106, 160, 134, 4, 128, 37, 145, 58, 82, 142, 161, 79, 116, 78, 85, 20, 57, 62, 104, 143, 46, 170, 156, 153, 6, 53, 39, 149, 88, 122, 137, 19, 29, 77, 51, 38, 23, 171, 67, 16, 111, 162, 52, 93, 68, 98, 1, 125, 17, 131, 109, 28, 91, 138, 127, 5, 94, 96, 119, 120, 147, 81, 8, 14, 108, 95, 24, 136, 12, 21, 27, 152, 44, 99, 140, 165, 124, 166, 86, 50, 148, 129, 73, 55, 35, 133, 66, 92, 163, 132,
0, 128, 53, 107, 57, 113, 40, 155, 116, 91, 50, 71, 62, 110, 54, 23, 24, 67, 92, 136, 1, 31, 132, 174, 111, 48, 46, 12, 104, 106, 114, 162, 95, 73, 153, 137, 18, 168, 38, 39, 147, 60, 178, 157, 82, 150, 142, 32, 160, 45, 177, 151, 156, 173, 7, 84, 87, 109, 101, 94, 159, 8, 44, 33, 51, 167, 169, 14, 63, 35, 117, 78, 138, 3, 43, 36, 154, 164, 28, 118, 140, 49, 27, 133, 77, 61, 100, 80, 161, 19, 85, 172, 29, 10, 64, 2, 171, 139, 146, 55, 16, 69, 56, 34, 21, 13, 124, 25, 4, 131, 158, 11, 144, 98, 47, 17, 96, 115, 26, 58, 9, 72, 163, 37, 176, 134, 126, 99, 123, 141, 42, 127, 89, 90, 166, 121, 135, 145, 15, 108, 165, 119, 75, 122, 149, 76, 148, 103, 152, 79, 59, 88, 112, 130, 93, 129, 70, 86, 97, 30, 20, 105, 125, 120, 6, 66, 68, 102, 170, 65, 143, 22, 41, 52, 74, 175, 81, 83, 5,
0, 136, 150, 113, 18, 12, 164, 110, 171, 49, 41, 163, 137, 149, 51, 109, 135, 76, 54, 142, 29, 35, 132, 152, 8, 112, 162, 72, 158, 44, 69, 16, 77, 13, 144, 170, 157, 87, 133, 43, 1, 66, 80, 75, 67, 70, 90, 11, 3, 27, 98, 178, 126, 82, 141, 96, 148, 39, 168, 64, 61, 155, 115, 124, 165, 28, 167, 26, 21, 94, 79, 106, 180, 160, 47, 17, 48, 57, 159, 7, 84, 172, 38, 81, 14, 85, 108, 114, 121, 78, 52, 63, 45, 125, 107, 127, 60, 89, 68, 92, 179, 73, 102, 19, 103, 74, 140, 161, 9, 105, 46, 31, 5, 2, 65, 174, 32, 101, 151, 123, 104, 91, 175, 25, 23, 93, 131, 53, 10, 111, 129, 99, 143, 88, 97, 22, 145, 33, 37, 147, 154, 34, 122, 156, 40, 24, 134, 15, 71, 130, 177, 30, 83, 36, 138, 139, 146, 173, 120, 4, 55, 59, 20, 116, 176, 128, 62, 86, 118, 153, 119, 56, 50, 117, 95, 169, 6, 166, 100, 58, 42,
0, 51, 19, 21, 177, 46, 91, 38, 36, 128, 50, 58, 71, 22, 189, 66, 119, 178, 23, 159, 123, 77, 165, 156, 162, 67, 47, 108, 16, 90, 161, 187, 169, 175, 111, 89, 118, 2, 6, 45, 103, 98, 42, 15, 157, 83, 28, 12, 133, 14, 150, 53, 99, 107, 31, 76, 113, 70, 151, 163, 33, 182, 147, 85, 4, 100, 37, 153, 96, 174, 155, 39, 40, 44, 171, 27, 1, 88, 7, 82, 124, 129, 8, 125, 80, 112, 166, 93, 61, 101, 81, 73, 152, 26, 92, 130, 43, 59, 62, 56, 5, 57, 69, 86, 110, 95, 84, 68, 109, 49, 117, 132, 173, 29, 139, 94, 35, 116, 75, 183, 87, 65, 104, 9, 142, 131, 3, 10, 41, 143, 140, 179, 72, 180, 185, 167, 138, 188, 149, 11, 134, 137, 141, 79, 127, 18, 158, 160, 30, 55, 13, 115, 170, 97, 126, 122, 144, 172, 145, 32, 24, 48, 114, 190, 148, 135, 52, 74, 17, 164, 105, 186, 60, 176, 181, 54, 63, 136, 120, 168, 146, 106, 184, 154, 121, 34, 64, 102, 20, 78, 25,
0, 39, 116, 3, 120, 49, 69, 165, 99, 187, 10, 30, 143, 181, 179, 117, 106, 64, 156, 145, 163, 90, 71, 72, 86, 83, 123, 131, 25, 107, 65, 23, 110, 50, 155, 125, 45, 8, 126, 35, 26, 20, 132, 24, 98, 12, 32, 115, 95, 67, 37, 101, 149, 62, 81, 139, 57, 127, 122, 152, 144, 186, 192, 70, 84, 111, 94, 182, 75, 9, 52, 138, 160, 61, 167, 121, 40, 17, 157, 27, 100, 19, 59, 16, 105, 166, 56, 191, 142, 76, 66, 150, 102, 130, 15, 91, 159, 172, 78, 97, 140, 133, 58, 38, 60, 18, 169, 47, 7, 174, 82, 162, 134, 190, 158, 4, 96, 148, 85, 77, 28, 63, 118, 41, 79, 55, 44, 36, 184, 104, 43, 89, 88, 128, 180, 2, 141, 178, 53, 34, 11, 168, 171, 68, 147, 129, 14, 29, 93, 173, 135, 6, 113, 153, 92, 80, 136, 21, 5, 189, 51, 54, 33, 22, 87, 103, 151, 137, 185, 31, 124, 13, 114, 188, 42, 177, 73, 170, 154, 46, 119, 164, 175, 1, 48, 146, 183, 109, 74, 176, 108, 161, 112,
0, 80, 134, 123, 82, 15, 9, 112, 6, 36, 102, 106, 42, 47, 28, 156, 41, 52, 158, 174, 37, 66, 59, 186, 7, 63, 58, 23, 111, 110, 44, 172, 43, 124, 34, 24, 130, 81, 115, 30, 27, 90, 177, 129, 182, 73, 133, 116, 136, 101, 35, 92, 12, 183, 31, 18, 170, 191, 121, 140, 119, 46, 161, 120, 13, 98, 64, 76, 60, 180, 125, 185, 176, 173, 79, 105, 49, 153, 17, 3, 16, 181, 70, 108, 57, 61, 4, 159, 67, 194, 56, 83, 107, 84, 195, 137, 178, 95, 175, 72, 50, 39, 19, 88, 169, 54, 126, 142, 118, 51, 188, 147, 69, 29, 103, 166, 184, 113, 25, 196, 150, 167, 135, 32, 45, 75, 99, 89, 5, 93, 154, 171, 71, 48, 86, 20, 14, 132, 2, 117, 74, 10, 145, 77, 162, 40, 151, 128, 187, 138, 8, 141, 100, 62, 53, 22, 143, 193, 26, 1, 146, 163, 127, 152, 139, 157, 189, 104, 179, 11, 168, 190, 33, 192, 122, 164, 97, 144, 21, 55, 85, 38, 165, 91, 78, 160, 109, 68, 148, 114, 149, 96, 131, 155, 94, 87, 65,
0, 60, 186, 27, 28, 58, 119, 43, 55, 159, 16, 148, 158, 110, 49, 50, 144, 42, 25, 107, 10, 98, 157, 180, 59, 116, 67, 108, 102, 70, 149, 156, 154, 71, 118, 91, 128, 56, 123, 45, 127, 54, 198, 134, 26, 165, 17, 160, 35, 52, 117, 46, 84, 22, 115, 194, 18, 80, 153, 15, 111, 93, 64, 151, 188, 136, 90, 196, 4, 95, 92, 131, 183, 101, 48, 82, 124, 39, 104, 126, 31, 121, 57, 29, 113, 24, 30, 182, 152, 61, 88, 94, 181, 65, 172, 139, 8, 68, 175, 132, 81, 141, 12, 142, 146, 69, 120, 2, 191, 51, 23, 193, 100, 145, 97, 9, 99, 109, 32, 112, 130, 11, 44, 37, 77, 169, 147, 86, 20, 105, 38, 79, 75, 36, 125, 143, 166, 179, 178, 73, 133, 7, 170, 47, 135, 171, 62, 74, 76, 184, 103, 72, 161, 114, 173, 66, 197, 40, 19, 78, 192, 33, 87, 185, 176, 122, 168, 14, 89, 140, 164, 155, 1, 3, 13, 96, 5, 129, 106, 162, 85, 190, 41, 189, 187, 163, 6, 34, 21, 177, 63, 137, 53, 83, 150, 167, 138, 174, 195,
0, 32, 27, 44, 106, 160, 39, 22, 139, 7, 151, 156, 75, 1, 109, 182, 94, 158, 28, 163, 55, 23, 40, 29, 170, 118, 58, 193, 196, 41, 60, 53, 34, 124, 186, 171, 16, 120, 179, 111, 64, 138, 83, 142, 176, 68, 35, 198, 5, 85, 175, 130, 205, 153, 159, 30, 24, 125, 105, 128, 51, 197, 195, 202, 56, 17, 59, 104, 95, 181, 69, 188, 180, 38, 185, 88, 161, 207, 20, 57, 96, 89, 25, 98, 36, 15, 2, 70, 203, 121, 187, 114, 9, 209, 79, 149, 101, 129, 86, 168, 12, 112, 148, 126, 210, 144, 76, 81, 37, 19, 172, 63, 141, 201, 206, 127, 194, 145, 133, 122, 150, 131, 208, 119, 13, 10, 154, 136, 31, 117, 80, 74, 189, 99, 169, 93, 164, 132, 155, 174, 190, 152, 92, 67, 103, 199, 4, 140, 11, 26, 47, 135, 167, 183, 8, 77, 48, 110, 45, 147, 3, 82, 52, 91, 90, 102, 184, 62, 54, 157, 61, 192, 21, 97, 6, 108, 113, 123, 87, 200, 78, 137, 84, 66, 134, 178, 173, 204, 146, 49, 71, 46, 177, 116, 72, 115, 107, 100, 50, 191, 165, 14, 73, 65, 43, 143, 18, 42, 162, 166, 33,
0, 102, 60, 188, 48, 216, 218, 100, 31, 160, 115, 180, 111, 126, 170, 61, 185, 69, 51, 6, 43, 165, 175, 206, 28, 49, 12, 74, 191, 32, 101, 150, 154, 173, 96, 4, 50, 147, 141, 109, 55, 113, 104, 208, 119, 35, 40, 81, 58, 11, 103, 201, 220, 199, 13, 1, 212, 39, 164, 92, 130, 41, 137, 190, 33, 143, 120, 25, 54, 62, 196, 194, 192, 168, 171, 152, 174, 122, 179, 221, 183, 222, 47, 169, 44, 21, 149, 5, 187, 76, 133, 86, 181, 148, 184, 118, 2, 108, 7, 116, 45, 24, 163, 156, 110, 121, 210, 77, 193, 36, 80, 202, 3, 124, 17, 79, 70, 145, 209, 59, 131, 22, 140, 73, 112, 97, 91, 87, 139, 16, 107, 98, 205, 189, 214, 72, 151, 211, 177, 138, 56, 29, 99, 157, 114, 195, 153, 66, 93, 161, 128, 207, 125, 89, 105, 215, 14, 155, 88, 57, 217, 90, 9, 53, 158, 172, 95, 8, 85, 136, 52, 20, 213, 67, 15, 176, 64, 127, 19, 37, 106, 38, 71, 75, 34, 123, 78, 82, 204, 144, 84, 30, 134, 182, 65, 219, 18, 83, 94, 129, 27, 159, 135, 203, 162, 46, 200, 142, 63, 117, 26, 186, 167, 23, 197, 178, 42, 198, 166, 146, 68, 10, 132,
0, 196, 6, 44, 126, 38, 148, 81, 215, 207, 134, 136, 5, 69, 145, 123, 88, 33, 138, 77, 213, 211, 112, 119, 116, 141, 206, 200, 188, 78, 92, 9, 96, 80, 137, 226, 18, 108, 41, 28, 210, 161, 115, 8, 7, 168, 49, 82, 95, 156, 162, 223, 130, 91, 16, 75, 58, 221, 172, 224, 201, 102, 114, 153, 194, 30, 14, 29, 209, 170, 169, 84, 21, 181, 86, 127, 208, 165, 99, 160, 222, 135, 149, 10, 59, 27, 216, 147, 66, 113, 93, 154, 133, 100, 42, 103, 55, 124, 74, 68, 220, 13, 101, 36, 129, 63, 204, 131, 184, 163, 53, 150, 120, 15, 2, 46, 24, 104, 110, 174, 72, 65, 142, 185, 173, 11, 186, 107, 34, 166, 171, 73, 177, 22, 32, 205, 118, 203, 146, 125, 23, 47, 128, 195, 219, 193, 121, 1, 191, 70, 143, 50, 117, 183, 202, 151, 178, 40, 79, 140, 106, 71, 26, 132, 48, 39, 182, 52, 87, 37, 97, 157, 105, 64, 158, 57, 167, 85, 61, 189, 164, 225, 35, 197, 51, 98, 111, 187, 198, 190, 83, 45, 90, 199, 43, 152, 176, 19, 76, 139, 214, 218, 20, 62, 25, 67, 60, 179, 175, 144, 94, 109, 155, 54, 212, 180, 56, 217, 89, 12, 17, 192, 3, 4, 159, 122, 31,
0, 146, 105, 165, 73, 51, 94, 178, 127, 112, 144, 102, 120, 20, 24, 44, 12, 129, 76, 133, 140, 224, 183, 106, 203, 118, 97, 148, 13, 37, 98, 186, 82, 48, 32, 53, 121, 166, 26, 124, 59, 66, 157, 87, 31, 114, 40, 192, 185, 93, 1, 141, 184, 205, 136, 193, 206, 109, 62, 182, 174, 8, 196, 110, 145, 29, 6, 100, 150, 54, 64, 188, 55, 163, 117, 135, 169, 191, 228, 210, 19, 99, 10, 154, 128, 46, 101, 16, 77, 47, 180, 197, 67, 131, 152, 42, 211, 103, 74, 43, 221, 204, 95, 34, 130, 160, 45, 79, 90, 36, 22, 80, 173, 115, 56, 147, 17, 83, 33, 91, 156, 223, 11, 61, 217, 227, 164, 75, 218, 214, 69, 168, 25, 143, 27, 63, 41, 57, 126, 134, 179, 4, 194, 21, 60, 28, 202, 72, 162, 208, 71, 96, 52, 170, 35, 176, 7, 209, 84, 137, 107, 108, 58, 216, 142, 65, 161, 149, 111, 138, 122, 181, 70, 9, 190, 89, 158, 220, 139, 81, 175, 159, 78, 119, 132, 151, 39, 116, 30, 195, 68, 49, 88, 38, 86, 226, 177, 187, 123, 207, 167, 15, 200, 14, 199, 85, 113, 172, 125, 222, 215, 201, 5, 18, 23, 50, 198, 171, 2, 153, 104, 212, 189, 213, 155, 225, 219, 92, 3,
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